Theorems · Theorem · commutative algebra
Ideal.comap_bot_of_injective
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
[inst_3 : RingHomClass F R S], Function.Injective ⇑f → Ideal.comap f ⊥ = ⊥- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- FunLikestatement and proof · cited by 2,560
- Ideal.comapstatement · cited by 443
- RingHomClassstatement and proof · cited by 193
- le_bot_iffproof · cited by 116
- Ideal.comap_bot_le_of_injectiveproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.IsIntegral.comap_surjectiveproof · cited by 2
- IsLocalization.bot_lt_under_primeproof · cited by 2
- Ideal.under_botproof · cited by 2
- ValuationSubring.idealOfLE_topproof · cited by 0
- Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injectiveproof · cited by 0